Invariance Conditions for Random Curvature Models

Marlos A. G. Viana
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Marlos A. G. Viana: University of Illinois at Chicago

Methodology and Computing in Applied Probability, 2003, vol. 5, issue 4, 439-453

Abstract: Abstract A class of probability models is introduced with the objective of representing certain properties of the geometric optics of the human eye. Astigmatic probability laws are those in which the extreme curvature values in the anterior corneal surface, measured at circularly arranged and equally spaced locations, are displaced by an approximate 90 deg angular separation. The relationship between the symmetry invariance of these probability laws for curvature data and probability laws for the ranking permutations associated with the ordering of these data is obtained. A distinction is made between the condition in which the components of the curvature ensemble are represented as real numbers from that in which these curvatures are color-coded and take value on a finite totally ordered set. A constructive principle for astigmatic laws is outlined based on algebraic arguments for the analysis of structured data.

Keywords: corneal curvature; random permutations; matrices; symmetric group; structured data; orbits; keratometry (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (1)

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DOI: 10.1023/A:1026285429743

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